Analytical prediction of mode I strain energy release rate at crack growth initiation of polymeric nanocomposites

In this paper, the effect of carbon nanotubes on mode I strain energy release rate at crack growth initiation of epoxy-based nanocomposites was studied analytically. In this theoretical model, effect of carbon nanotubes debonding from its surrounding resin at the crack tip was postulated as one of the causes of increasing of the strain energy release rate of nanocomposites in comparison with the pure resin. Furthermore, a representative volume element was considered at the nanoscale. The assumed representative volume element contains carbon nanotubes, surrounding resin and the interphase. The available mechanical properties and the thickness of the interphase in the literature were used. Finally, a model for increasing the strain energy release rate of nanocomposites due to presence of carbon nanotubes was introduced based on mechanical properties and geometric parameters of carbon nanotubes and resin. It must be noted that enhancement of strain energy release rate in comparison with the pure polymer was investigated by correlation between nano, micro and macro-scales. To validate the proposed analytical model, results were compared with other experimental results available in the literature. The results show that the present model has a reasonable error and is able to model the effect of single-wall and multi-wall carbon nanotubes on nanocomposites strain energy release rate.